Find a positive value of \(\alpha\) if the coordinate of the centre of a circle x\(^2\) + y\(^2\) – 2\(\alpha\)x + 4y – \(\alpha\) = 0 is (\(\alpha\), -2) and the radius is 4 units.
- A. 1
- B. 2
- C. 3
- D. 4
Divide 4x\(^3\) – 3x + 1 by 2x – 1
- A. 2x2-x+1
- B. 2x2-x-1
- C. 2x2+x+1
- D. 2x2+x-1
The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.
- A. 8/5
- B. 8/3
- C. 72/25
- D. 56/9
Express \(\frac{1}{x^{3}-1}\) in partial fractions
- A. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x + 2)}{x^{2} + x + 1})\)
- B. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{x - 2}{x^{2} + x + 1})\)
- C. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 2)}{x^{2} + x + 1})\)
- D. \(\frac{1}{3}(\frac{1}{x - 1} - \frac{(x - 1)}{x^{2} - x - 1})\)
Three consecutive positive integers k, l and m are such that l\(^2\) = 3(k+m). Find the value of m.
- A. 4
- B. 5
- C. 6
- D. 7
Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.
- A. 4≤X≤5
- B. 5≤X≤8
- C. 5≤X≤10
- D. 8≤X≤10
Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y – 18\).
- A. (x+y+6)(x+y-3)
- B. (x-y-6)(x-y+3)
- C. (x-y+6)(x-y-3)
- D. (x+y-6)(x+y+3)
A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
- A. 2/3
- B. 1/2
- C. -1/2
- D. -2/3
The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
- A. p/2
- B. 3p/2
- C. 5p/2
- D. 3p
If \(m*n = (\frac{m}{n} – \frac{n}{m}\)) for m, n belong to R, evaluate -3*4
- A. \(\frac{-25}{12}\)
- B. \(\frac{-7}{12}\)
- C. \(\frac{7}{12}\)
- D. \(\frac{25}{12}\)
Simplify \(\sqrt{\frac{(0.0023 \times 750)}{(0.00345 \times 1.25)}}\)
- A. 15
- B. 20
- C. 40
- D. 75
If 2\(_9\) x (Y3)\(_9\) = 3\(_5\) x (Y3)\(_5\), find the value of Y.
- A. 4
- B. 3
- C. 2
- D. 1
What is the answer when 2434\(_6\) is divided by 42\(_6\)?
- A. 236
- B. 356
- C. 526
- D. 556
A trader bought 100 oranges at 5 for N1.20, 20 oranges got spoilt and the remaining were sold at 4 for N1.50. Find the percentage gain or loss.
- A. 30% gain
- B. 25% gain
- C. 30% loss
- D. 25% loss
If \(\frac{({a^2b^{-3}c})^{3/4}}{a^{-1}b^4c^5}\) = \(a^p b^q c^r\); what is the value of p+2q?
- A. (5/2)
- B. -(5/4)
- C. -(25/4)
- D. -10
If \(\frac{(a^2 b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^{4}c^{5}}=a^{p} b^{q} c^{r}\) What is the value of p+2q?
- A. (5/2)
- B. -(5/4)
- C. -(25/4)
- D. -10
Find the value of X if \(\frac{\sqrt{2}}{x+\sqrt{2}}=\frac{1}{x-\sqrt{2}}\)
- A. 3√2+4
- B. 3√2-4
- C. 3-2√2
- D. 4+2√2
If log\(_810\) = X, evaluate log\(_85\) in terms of X.
- A. \(\frac{1}{2}\)X
- B. X-\(\frac{1}{4}\)
- C. X-\(\frac{1}{3}\)
- D. X-\(\frac{1}{2}\)
A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?
- A. 25
- B. 19
- C. 18
- D. 17